A classic Tesla coil consists of two inductive-capacitive (LC) oscillators,
loosely coupled to one another. An LC oscillator has two main components,
an inductor (which has inductance, L measured in Henrys) and a capacitor
(with capacitance C measured in Farads). An inductor converts an electrical
current (symbol I, measured in Amperes) into a magnetic field (symbol B,
measured in Tesla [yes, named in honor of Nikola Tesla]), or a magnetic
field into a current. Inductors are formed from electrical conductors wound
into coils. Capacitors consist of two or more conductors separated by an
insulator. A capacitor converts current into an electric field (symbol
V, measured in Volts) or an electric field into current. Both magnetic
fields and electric fields are forms of stored energy (symbol U, measured
in Joules). When a charged capacitor (U=CV2/2) is connected
to an inductor an electric current will flow from the capacitor through
the inductor creating a magnetic field (U=LI2/2). When the electric
field in the capacitor is exhausted the current stops and the magnetic
field collapses. As the magnetic field collapses, it induces a current
to flow in the inductor in the opposite direction to the original current.
This new current charges the capacitor, creating a new electric field,
equal but opposite to the original field. As long as the inductor and capacitor
are connected the energy in the system will oscillate between the magnetic
field and the electric field as the current constantly reverses. The rate
(symbol [Greek nu], cycles per second or Hertz) at which the system oscillates
is given by (the square root of 1/LC)/2pi. One full cycle of oscillation
is shown in the drawing below. In the real world the oscillation will eventually
damp out due to resistive losses in the conductors (the energy will be
dissipated as heat).

In a Tesla coil, the two inductors share the same axis and are located
close to one another. In this manner the magnetic field produced by one
inductor can generate a current in the other. The schematic below shows
the basic components of a Tesla coil. The primary oscillator consists of
a flat spiral inductor with only a few turns, a capacitor, a voltage source
to charge the capacitor and a switch to connect the capacitor to the inductor.
The secondary oscillator contains a large, tightly wound inductor with
many turns and a capacitor formed by the earth on one end (the base) and
an output terminal (usually a sphere or toroid) on the other.

While the switch is open, a low current (limited by the source) flows
through the primary inductor, charging the capacitor. When the switch is
closed a much higher current flows from the capacitor through the primary
inductor. The resulting magnetic field induces a corresponding current
in the secondary. Because the secondary contains many more turns than the
primary a very high electric field is established in the secondary capacitor.
The output of a Tesla coil is maximized when two conditions are met. First,
both the primary and secondary must oscillate at the same frequency. And
secondly, the total length of conductor in the secondary must be equal
to one quarter of the oscillator's wave length. Wave length (Greek lambda,
in meters) is equal to the speed of light (300,000,000 meters per second)
divided by the frequency of the oscillator.

Tesla coils differ in the type of switch used, the physical size of
the components and the input voltage. Automotive ignition coils typically
have a twelve volt input and are switched by a distributor, with moving
contacts. They provide an output of 15-20,000 volts. Television fly-back
transformers produce lower outputs but usually have 120 volt inputs and
are switched by transistors or, in very old sets, vacuum tubes. The classic
Tesla coil is switched by a spark gap. In this case, the primary circuit
is known as a tank circuit. In its simplest form, the spark gap switch
has two conductors separated by an air gap. When the electric field stored
in the capacitor reaches a level sufficient to ionize the air within the
gap a highly conductive plasma is formed, effectively closing the switch.
Spark gap switched coils operate with inputs of about 5-20,000 volts and
produce outputs of 100,000 to several million volts. For the spark gap
to be effective, it must be able to open rapidly after the primary oscillation
has damped out, in order that the capacitor may recharge. This is achieved
by several methods, all of which amount to ways of cooling and dissipating
the hot plasma formed during conduction. The simple gap can switch a few
hundred watts of input power. Forced air cooling of the gap and, or using
a number of gaps in series can increase power handling to several thousand
watts. Higher power levels usually require a rotary gap, which mechanically
moves gap electrodes rapidly into and out of conduction range. I should
note here that even at input power levels of a thousand watts, the instantaneous
power levels during gap firing can reach a million watts or more.